Question

Question about derivative test :

I'm doing homework where it asks me to find the max or min through a second derivative test. The second derivative of this function however is a positive constant. Does that mean that I have a minimum ?

Answer 1

Yep

Answer 2

@FaiqRaees

Okay so the problem I have is that there's a 100cm wire is cut into two pieces, one is bent to form the shape of an equilateral triangle and the other a square.

if my second derivative is a constant how do I find the where we could cut the wire for the minimum?

Answer 3

see u have to put the first derivative test to zero

Answer 4

equate dy/dx to 0

Answer 5

Sorry for the typing. I'm on a spazz lol

Answer 6

I already found the first derivative, and when I did the second I got a constant @kanwal32

Answer 7

did u got the constant greater than zero or less than zero????

Answer 8

greater than 0

Answer 9

then it will give minimum no need to put the values

Answer 10

also got a crit value of 56.5 btw

Answer 11

okay so the minimum on where to cut the wire is what the 2nd derivative is ?

Answer 12

no it is the first derivative

Answer 13

u have to minimize the area

Answer 14

now put dy/dx=0

Answer 15

did u get -100 / sqrt(3) ?

Answer 16

sorry i got this wrong

Answer 17

i am now doing it correctly

Answer 18

It's okay

Answer 19

let side of triangle is x and side of square be y

Answer 20

perimeter of triangle + perimeter of square=total wire length

Answer 21

are u getting this

Answer 22

okay so like this ? f := ((100-x)*(1/4))^2+(1/4)*sqrt(3)*((1/3)*x)^2

Answer 23

4y+3x=100
y=(100-3x)/4

Answer 24

yeah

Answer 25

area of square=y^2
(100-3x/4)^2

Answer 26

I got this one for the total length wire :

Answer 27

yes u are right

Answer 28

when I set that to 0 I got

Answer 29

So that is where the wire is cut?

Answer 30

yes

Answer 31

Awesome. And how di find the max area ?

Answer 32

i think your x value is wrong

Answer 33

why? shouldi get more than one answer?

Answer 34

can u show me the equation where u put x=0

Answer 35

im doing this through maple so its gnna look kinda weird

Answer 36

in the first derivative

Answer 37

I think I figured it out. Thanks for the help @kanwal32 :)

Answer 38

if u got x=that
then plug into the y equation to get maximum area

Answer 39

into the first equaiton

Answer 40

@vheah